Object not visible in render even when it is not disabled in rendering
Not a whole answer: I've figured out what happens, but not why. I thought it best to share it anyway since it might help.
In the 3D Viewport the object seems to be affected by the Surface Deform modifier. But for rendering it is not. When rendered it is in the shape (and location) where it would be without the Surface Deform modifier.
If you render the character from the back you can see the object in this location, partly hidden in the body of the character.

A possible solution is to Apply the the Surface Deform modifier on the object.